Question

Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers. ln(

3

y
2
z
6

​

x
2

​
)= help (formulas)

Answer 1

To rewrite the expression ln(3y^2z^6x^2) using sums and/or differences of logarithmic expressions that do not contain the logarithms of products, quotients, or powers, we can apply the laws of logarithms.

1. Start by breaking down the given expression into individual logarithms using the properties of logarithms:

ln(3) + ln(y^2) + ln(z^6) + ln(x^2)

2. Simplify each logarithm using the power rule of logarithms:

ln(3) + 2ln(y) + 6ln(z) + 2ln(x)

Now, the expression ln(3y^2z^6x^2) is written as a sum of logarithmic expressions without any logarithms of products, quotients, or powers.